Trim about 1/2 inch from the top and bottom of each parsnip. Scrub the parsnips well but do not peel.

Bring a large saucepan of water to a boil over high heat. Add the parsnips. Cover, reduce the heat to medium-low, and cook until very tender, 25 to 30 minutes. Test for doneness by inserting the tip of a sharp knife into a parsnip.

Remove the parsnips with tongs, and place on a clean work surface. Set the cooking water aside.

Using a paper towel to protect your fingers, hold each parsnip by the end, and scrape off the skin with a small paring knife or vegetable peeler. Discard the skin. Place the parsnips in a large bowl.

Add the sour cream, allspice, salt, and 2 tablespoons of the reserved cooking liquid. With a potato masher or fork, coarsely mash the parsnips. Add 1 to 3 more tablespoons of cooking liquid if necessary to make the mixture smooth and creamy.

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